I'm trying to solve a relatively small sparse matrix (about 5000 by 5000 with 13000 non-zero numbers) using SuiteSparse C++ library. The matrix happens to be symmetric positive definite, so I tried both KLU and CHOLMOD routines. When timing the clock time of numeric and symbolic factorization step for both routines, I found that the time both routines take are quite similar.
This result is not what I expect, since generally cholesky factorization takes half time of LU factorization in the factorization step. I'm wondering if this observation is reasonable? Possibly due to the fact that the matrix is relatively small? I'm not sure if there are any implementation detail I ignored that results in this behavior.
KLU:
klu_symbolic* s = klu_analyze(n, Ap, Ai, common);
klu_numeric* c = klu_factor(Ap, Ai, Ax, s, common)
CHOLMOD:
cholmod_factor* L = cholmod_analyze(A, common);
cholmod_factorize(A, L, common);
Any help is appreciated!